Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you graph the inequality 2x + 3 < 7?

Back

First, solve for x: 2x < 4, so x < 2. Graph a number line with an open circle at 2 and shade to the left.

Front

When graphing the inequality x < 3, what type of circle is used?

Back

An open circle is used for '<' because 3 is not included in the solution.

Front

What is the first step to solve the inequality 84 - 4x ≤ 52?

Back

Subtract 84 from both sides: -4x ≤ -32.

Front

How do you isolate x in the inequality -4x ≤ -32?

Back

Divide both sides by -4, remembering to flip the inequality sign: x ≥ 8.

Front

In the context of inequalities, what does 'at least' mean?

Back

'At least' means the value must be greater than or equal to a certain number.